Relative Moving Charge: Electric vs Magnetic Field

[jmnance]

So what is the answer to "if I am moving at velocity v with respect to a single charge, charge q, will I see the electric field as I would at rest with respect to the charge, or will I see a magnetic field? what will be the strength of the magnetic field?"

 

[pmb_phy]

So what is the answer to "if I am moving at velocity v with respect to a single charge, charge q, will I see the electric field as I would at rest with respect to the charge, or will I see a magnetic field? what will be the strength of the magnetic field?"

You will observe a magnetic field which has the value

B = -$\gamma$$\beta$xE

where E is the electric field as measured in the charges rest frame. Note: that $\beta$ is supposed to be in bold because its a vector.

Pete

 

[Entropia]

The answer to this question depends on the direction of the velocity v with respect to the charge q. If the velocity v is parallel to the direction of the charge q, then you will see the electric field as you would at rest with respect to the charge. This is because the electric field is caused by the presence of a stationary charge and is not affected by the motion of the observer.

However, if the velocity v is perpendicular to the direction of the charge q, then you will see both an electric field and a magnetic field. This is known as the Lorentz transformation and is a result of the relative motion between the observer and the charge.

The strength of the magnetic field will depend on the velocity v and the charge q. It is given by the equation B = (μ0qv)/4πr, where μ0 is the permeability of free space, q is the charge, v is the velocity, and r is the distance between the charge and the observer. As the velocity v increases, the strength of the magnetic field also increases.

In summary, if you are moving at velocity v with respect to a single charge q, you will see both an electric field and a magnetic field. The strength of the magnetic field will depend on the velocity v and the charge q, and it will be stronger as the velocity increases.